In this homework, you are expected to implement the following programs using recursion.
- 1) We have bunnies standing in a line, numbered 1, 2, … The odd bunnies (1, 3, ..) have the normal 2 ears. The even bunnies (2, 4, ..) have 3 ears, because they each have a raised foot. Recursively return the number of “ears” in the bunny line 1, 2, … n (without loops or multiplication).
Example:
Please enter the number of lines (n=): 2 bunnyEars2(0) → 0
bunnyEars2(1) → 2
bunnyEars2(2) → 5 - 2) In this question, you will write a program to find super digit of a number X using the following rules:
- If X has only 1 digit, then its super digit is X.
- If X has more than 1 digit, then its super digit is equal to the super digit of the digit-sum of X.
Example:
superDigit(1245)
• The number X will be given to your program with two numbers (n and k) and you will construct the number X as the number n concatenated k times.
Example:
Please enter a number (n=) : 123
Please enter repetition factor (k=) : 3 Super digit of number 123123123 is 9.
= superDigit(1+2+4+5) = superDigit(12) = superDigit(1+2) = superDigit(3)
= 3.
3) In this question, you will print identical triangles nested each other recursively. You will construct the triangles by using two digits ‘_’(underscore) and ‘1’. There will be number of iterations given as an input to your program.
• If the number of iterations is given as 0, you will print a simple triangle by using 32 rows and 63 columns in a matrix as the following:
_______________________________1_______________________________ ______________________________111______________________________ _____________________________11111_____________________________ ____________________________1111111____________________________ ___________________________111111111___________________________ __________________________11111111111__________________________ _________________________1111111111111_________________________ ________________________111111111111111________________________ _______________________11111111111111111_______________________ ______________________1111111111111111111______________________ _____________________111111111111111111111_____________________ ____________________11111111111111111111111____________________ ___________________1111111111111111111111111___________________ __________________111111111111111111111111111__________________ _________________11111111111111111111111111111_________________ ________________1111111111111111111111111111111________________ _______________111111111111111111111111111111111_______________ ______________11111111111111111111111111111111111______________ _____________1111111111111111111111111111111111111_____________ ____________111111111111111111111111111111111111111____________ ___________11111111111111111111111111111111111111111___________ __________1111111111111111111111111111111111111111111__________ _________111111111111111111111111111111111111111111111_________ ________11111111111111111111111111111111111111111111111________ _______1111111111111111111111111111111111111111111111111_______ ______111111111111111111111111111111111111111111111111111______ _____11111111111111111111111111111111111111111111111111111_____ ____1111111111111111111111111111111111111111111111111111111____ ___111111111111111111111111111111111111111111111111111111111___ __11111111111111111111111111111111111111111111111111111111111__ _1111111111111111111111111111111111111111111111111111111111111_ 111111111111111111111111111111111111111111111111111111111111111
• If the number of iterations is given as 1, you will create 3 triangles by calculating their 3 corner points using the original triangle in the previous iteration. It should be noted that the original triangle at iteration 0 will be decomposed three identical triangles as the following:
_______________________________1_______________________________ ______________________________111______________________________ _____________________________11111_____________________________ ____________________________1111111____________________________ ___________________________111111111___________________________ __________________________11111111111__________________________ _________________________1111111111111_________________________ ________________________111111111111111________________________ _______________________11111111111111111_______________________ ______________________1111111111111111111______________________ _____________________111111111111111111111_____________________ ____________________11111111111111111111111____________________ ___________________1111111111111111111111111___________________ __________________111111111111111111111111111__________________ _________________11111111111111111111111111111_________________ ________________1111111111111111111111111111111________________ _______________1_______________________________1_______________ ______________111_____________________________111______________ _____________11111___________________________11111_____________ ____________1111111_________________________1111111____________ ___________111111111_______________________111111111___________ __________11111111111_____________________11111111111__________ _________1111111111111___________________1111111111111_________ ________111111111111111_________________111111111111111________ _______11111111111111111_______________11111111111111111_______ ______1111111111111111111_____________1111111111111111111______ _____111111111111111111111___________111111111111111111111_____ ____11111111111111111111111_________11111111111111111111111____ ___1111111111111111111111111_______1111111111111111111111111___ __111111111111111111111111111_____111111111111111111111111111__ _11111111111111111111111111111___11111111111111111111111111111_ 1111111111111111111111111111111_1111111111111111111111111111111
• If the number of iterations is given as 2, you will again create 3 triangles for each triangle in the previous iteration by calculating their 3 corner points using the triangles in the previous iteration. It should be noted that each triangle at iteration 1 will be decomposed three identical triangles as the following:
_______________________________1_______________________________ ______________________________111______________________________ _____________________________11111_____________________________ ____________________________1111111____________________________ ___________________________111111111___________________________ __________________________11111111111__________________________ _________________________1111111111111_________________________ ________________________111111111111111________________________ _______________________1_______________1_______________________ ______________________111_____________111______________________ _____________________11111___________11111_____________________ ____________________1111111_________1111111____________________ ___________________111111111_______111111111___________________ __________________11111111111_____11111111111__________________ _________________1111111111111___1111111111111_________________ ________________111111111111111_111111111111111________________ _______________1_______________________________1_______________ ______________111_____________________________111______________ _____________11111___________________________11111_____________ ____________1111111_________________________1111111____________ ___________111111111_______________________111111111___________ __________11111111111_____________________11111111111__________ _________1111111111111___________________1111111111111_________ ________111111111111111_________________111111111111111________ _______1_______________1_______________1_______________1_______ ______111_____________111_____________111_____________111______ _____11111___________11111___________11111___________11111_____ ____1111111_________1111111_________1111111_________1111111____ ___111111111_______111111111_______111111111_______111111111___ __11111111111_____11111111111_____11111111111_____11111111111__ _1111111111111___1111111111111___1111111111111___1111111111111_ 111111111111111_111111111111111_111111111111111_111111111111111
• If the number of iterations is given as 3, you will need to print triangles as the following:
_______________________________1_______________________________ ______________________________111______________________________ _____________________________11111_____________________________ ____________________________1111111____________________________ ___________________________1_______1___________________________ __________________________111_____111__________________________ _________________________11111___11111_________________________ ________________________1111111_1111111________________________ _______________________1_______________1_______________________ ______________________111_____________111______________________ _____________________11111___________11111_____________________ ____________________1111111_________1111111____________________ ___________________1_______1_______1_______1___________________ __________________111_____111_____111_____111__________________ _________________11111___11111___11111___11111_________________ ________________1111111_1111111_1111111_1111111________________ _______________1_______________________________1_______________ ______________111_____________________________111______________ _____________11111___________________________11111_____________ ____________1111111_________________________1111111____________ ___________1_______1_______________________1_______1___________ __________111_____111_____________________111_____111__________ _________11111___11111___________________11111___11111_________ ________1111111_1111111_________________1111111_1111111________ _______1_______________1_______________1_______________1_______ ______111_____________111_____________111_____________111______ _____11111___________11111___________11111___________11111_____ ____1111111_________1111111_________1111111_________1111111____ ___1_______1_______1_______1_______1_______1_______1_______1___ __111_____111_____111_____111_____111_____111_____111_____111__ _11111___11111___11111___11111___11111___11111___11111___11111_ 1111111_1111111_1111111_1111111_1111111_1111111_1111111_1111111
- If the number of iterations is given as 4, you will need to print triangles as the following:
_______________________________1_______________________________ ______________________________111______________________________ _____________________________1___1_____________________________ ____________________________111_111____________________________ ___________________________1_______1___________________________ __________________________111_____111__________________________ _________________________1___1___1___1_________________________ ________________________111_111_111_111________________________ _______________________1_______________1_______________________ ______________________111_____________111______________________ _____________________1___1___________1___1_____________________ ____________________111_111_________111_111____________________ ___________________1_______1_______1_______1___________________ __________________111_____111_____111_____111__________________ _________________1___1___1___1___1___1___1___1_________________ ________________111_111_111_111_111_111_111_111________________ _______________1_______________________________1_______________ ______________111_____________________________111______________ _____________1___1___________________________1___1_____________ ____________111_111_________________________111_111____________ ___________1_______1_______________________1_______1___________ __________111_____111_____________________111_____111__________ _________1___1___1___1___________________1___1___1___1_________ ________111_111_111_111_________________111_111_111_111________ _______1_______________1_______________1_______________1_______ ______111_____________111_____________111_____________111______ _____1___1___________1___1___________1___1___________1___1_____ ____111_111_________111_111_________111_111_________111_111____ ___1_______1_______1_______1_______1_______1_______1_______1___ __111_____111_____111_____111_____111_____111_____111_____111__ _1___1___1___1___1___1___1___1___1___1___1___1___1___1___1___1_ 111_111_111_111_111_111_111_111_111_111_111_111_111_111_111_111
- The number of iterations given to your program will be less than 5.
- The output will consist of 32 rows and 63 columns, and will be composed of ones (1) and
underscores (_) as in the triangles above.
- Solutions using iterations will not be graded for ALL questions.
- You have to solve the problems by using RECURSION.
- It should be noted that selected parts will be graded in your homework.
